Stocks, Bonds, And The Investment Horizon: Decision-making For The Long Run

494 Pages·2022·30.104 MB·English

by  Haim Levy

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World Scientific
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-Publication Data
Names: Levy, Haim, author.
Title: Stocks, bonds, and the investment horizon : decision-making for the long run /
Haim Levy, The Hebrew University of Jerusalem, Israel.
Description: Hackensack, NJ : World Scientific, [2022] |
Includes bibliographical references and index.
Identifiers: LCCN 2021055873 | ISBN 9789811250149 (hardcover) |
ISBN 9789811250156 (ebook) | ISBN 9789811250163 (ebook other)
Subjects: LCSH: Investments. | Stocks. | Bonds. | Portfolio management.
m Classification: LCC HG4521 .L6326 2022 | DDC 658.15/54--dc23/eng/20211213
co LC record available at https://lccn.loc.gov/2021055873
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e Copyright © 2022 by World Scientific Publishing Co. Pte. Ltd.
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Email: [email protected]
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To My Family
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Contents
Preface xiii
m Introduction 1
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d The Ongoing Disputes 15
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w. 1.1 The “Planned” and the “Actual” Investment
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w Horizons ............................................................... 16
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o 1.2 Dispute Number 1: Do Stocks Become Riskier or
ed fr Safer with the Horizon? . . . . . . . . . . . . . . . . . 21
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o Expected Utility Conflict for Investment for the
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Very Long Run ..................................................... 31
1.4 The Probability that a Stock’s Terminal Wealth
will be Larger than a Bond’s Terminal Wealth for
Various Finite Long Investment Horizons . . . . . . 40
1.5 Diversification Across Time — The Case for Target-
Date Funds .......................................................... 45
1.6 What is the Rationale for the Glide Path
Investment Strategy? ............................................ 52
1.7 Summary ............................................................... 60
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viii Stocks, Bonds, and the Investment Horizon
Chapter 2. The Distribution of Returns
and the Horizon 63
2.1 The Investment Horizon and Skewness:
The Theory .......................................................... 68
2.2 The Investment Horizon and Skewness:
The Best Fit Theoretical Distribution . . . . . . . . 81
2.3 Skewness and the Best Fit Distribution: Autocorrelation
is Incorporated . . . . . . . . . . . . 92
2.4 Summary ............................................................... 97
Chapter 3. Mean–Variance, Stochastic
Dominance, and the Investment Horizon 99
3.1 The M–V Rule and the Horizon . . . . . . . . . . . . 106
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o 3.2 The Multi-Period Variance as a Function of the
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cie 3.3 Stochastic Dominance Rules . . . . . . . . . . . . . . 118
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ed fr 3.7 The SSD Rule with One-Period Normal
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Distribution and the Horizon Effect . . . . . . . . . 142
3.9 The Economic Loss Induced by Employing the
M–V Rule for Long Horizons . . . . . . . . . . . . . . 145
3.10 The Arrow–Pratt Risk Premium and the
Investment Horizon .............................................. 154
3.11 Diversification: Markowitz’s Efficient Frontier in
the Multi-Period Case . . . . . . . . . . . . . . . . . . 157
3.12 The Multi-Period Variance Where Returns
May be Dependent Over Time: The Empirical
Evidence ............................................................... 161
3.13 Discussion ............................................................. 166
3.14 Summary ............................................................... 171
March31,2022 13:55 Stocks,Bonds,andtheInvestmentHorizon-9inx6in b4510-fm pageix
Contents ix
Chapter 4. Performance Indices and the
Investment Horizon 175
4.1 The Three Main Performance Indices:
Definitions ............................................................. 176
4.2 The Employment of the SR in Practice . . . . . . . 183
4.3 The One-Period and Multi-Period SRs:
Mathematical Analysis of Horizon Mismatch. . . . 185
4.4 The Changes in the Beta, Treynor Ration (TR),
and Jensen’s Alpha (JA) with the Increase
in the Horizon ..................................................... 204
4.5 The Changes in the Beta and the Performance
Indices with a Horizon Shorter than the CAPM
Horizon .................................................................. 213
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the Horizon .......................................................... 246
5.3 Asset Allocation and the Horizon in the
M–V Framework: The Empirical Evidence . . . . . 251
5.4 Optimal M–V Diversification with 10 Portfolios
of Risky Assets . . . . . . . . . . . . . . . . . . . . . . . 258
5.5 Contrasting the M–V and Expected Utility
Results for Various Horizons . . . . . . . . . . . . . . 262
5.6 Diversification: The Optimal Stock–Bond
Investment Weights for Various Utility
Functions ............................................................. 269
5.7 Summary ............................................................... 282